When Linda was 45 years old, her son was 2 times her daughter's age. Linda would be twice her son's age when her daughter was 27 years old. How old would Linda be when her daughter was 10 years old?

	Linda	Son	Daughter
Before	45	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	27

The difference in the ages between Linda and her son remains unchanged.

Difference in Linda's and her son's ages at first
45 - 2 u = 2 p - 1 p
45 - 2 u = 1 p --- (1)

The difference in the ages between her son and her daughter remains unchanged.

Difference in her son's and her daughter's ages at first
2 u - 1 u = 1 p - 27
1 u + 27 = 1 p --- (2)

Make p the same.

(1) = (2)
45 - 2 u = 1 u + 27
1 u + 2 u = 45 - 27
3 u = 18

1 u = 18 ÷ 3 = 6

Age difference between Linda and her daughter
= 45 - 1 u
= 45 - 6
= 39

Linda's age when her daughter was 10 years old
= 39 + 10
= 49

Answer(s): 49